Systems and methods for determining tooth center of resistance

ABSTRACT

A method and a system for determining a center of resistance point of a tooth for orthodontic treatment planning are provided. The method comprises: obtaining a tooth mesh from image data associated with a tooth crown of a patient; identifying a mesiodistal center of the tooth crown; determining a reference plane in the image data to extend through the mesiodistal center; determining an intersection curve based on an intersection of the reference plane and the tooth mesh, the intersection curve following a shape of the surface of the crown at the reference plane; determining a tooth axis of the tooth crown based on the intersection curve; determining a crown height of the tooth crown based on the tooth axis; and determining the center of resistance of the tooth based on the determined crown height and the determined tooth axis.

CROSS-REFERENCE

The present application is a continuation of U.S. patent applicationSer. No. 16/877,972 filed May 19, 2020, the entirety of which isincorporated by reference.

FIELD

The present technology relates to systems and methods for planning anorthodontic treatment for a patient, in general; and more specificallyto determining a center of resistance point (CR point) for patient'steeth.

BACKGROUND

In orthodontics, treatments for achieving alignment of malposed teeth ina patient include applying various orthodontic devices, such as alignersor braces that are configured to exert a force to the patient's teeth,thereby either causing the teeth to move or to a retain given position.In order to plan tooth movements in the course of a given orthodontictreatment, practitioners typically consider a plurality of referencepoints for applying forces exerted by the orthodontic devices.

One of such reference points is a resistance point (also known as aCenter of Resistance (CR) point) of a given tooth. In general, the giventooth is attached to an alveolar bone of one of a patient's maxilla (anupper jaw) and a patient's mandible (a lower jaw) by surroundingperiodontal tissue (also collectively referred to herein as “periodontalligament”). Thus, physically, the given tooth may be considered as abody restrained in the alveolar bone by forces applied by theperiodontal ligaments and neighboring teeth, for example, having itsassociated center of gravity (a center of mass). Accordingly, the CRpoint of the given tooth may be defined as its center of gravity. Tothat end, applying a force, at a given direction, to the CR point of thegiven tooth would result in a translation movement thereof.

Typically, the CR point is determined to be located on a tooth axis ofthe given tooth, which may be defined as an imaginary line extendingthrough a crown portion and a root portion of the given tooth, aroundwhich the given tooth is most symmetrically distributed. It will beappreciated that because of differences between teeth of a patient, andalso between teeth of different patients, the CR point will also varybetween teeth. Thus, a more accurate determination of the tooth axis ofthe given tooth and the CR point may provide for a more predictableplanning of the given orthodontic treatment for the patient. This mayfurther allow, for example, to accurately model some aspects of dynamicsof the given tooth in the course of the planned orthodontic treatmentusing, for example, a digital representation thereof. In this regard,the more accurate determination of the tooth axis and the CR point ofthe given tooth may further enable to achieve the object of the givenorthodontic treatment, that is, the alignment of the patient's teeth,more efficiently and effectively.

Certain prior art approaches have been proposed to address theabove-identified technical problem of determining the tooth axis basedon determining certain reference points associated with the crownportion and the root portion of the given tooth.

U.S. Pat. No. 8,512,037-B2 issued on Aug. 20, 2013, assigned to OrmcoCorp., and entitled “Custom Orthodontic Appliance System and Method”discloses various features for a custom orthodontic appliancemanufacturing or designing system. These include features for inputtingof data of patient anatomy and practitioner decisions, features forinteractively or automatically manipulating data to arrive at appliancecharacteristics, and features for affecting design or manufacture of theappliance.

United States Patent Application Publication No.: 2008/311,535-A1 filedon May 5, 2008, assigned to Ormco Corp., and entitled “TorqueOvercorrection Model” discloses a custom orthodontic appliance comprisedof brackets to be positioned on a patient's teeth, and an archwire, andis customized to provide a desired torque to a tooth by selecting anangle for the slot of at least one bracket so as to provide a torqueinteraction between that bracket slot and the archwire. The torqueinteraction is computed to compensate for tooth tilt resulting frommisalignment of the force vector applied by the archwire with the toothcenter of resistance. The torque interaction is computed at the desiredfinal position of the teeth, and may be computed to provide for anapplied torque even where the tooth is positioned in the desired finaltooth position to compensate for force diminution. Material propertiesof the archwire and the relative archwire slot geometry are evaluated todetermine an archwire/slot angular offset in which torque is applied tothe bracket.

U.S. Pat. No. 8,126,726-B2 issued on Feb. 28, 2012, assigned to AlignTechnology Inc., and entitled “System and Method for FacilitatingAutomated Dental Measurements and Diagnostics” discloses acquiring adigital model of a patient's teeth, automatically detecting referencedata or features based on the digital model, and automatically computingdental measurements based on said reference data or features, where thedental measurements are associated with an occlusal characteristic ofthe patient are disclosed.

SUMMARY

It is an object of the present technology to ameliorate at least some ofthe inconveniences present in the prior art.

The developers of the present technology have realized that determiningthe tooth axis for the given tooth may be performed more accurately whenconsidering certain specifics of the crown portion of the given tooth.Specifically, the developers have devised a method directed togenerating the tooth axis based on a reference plane intersecting thecrown portion of the given tooth perpendicular to a mesiodistaldirection associated therewith. Further, based on so determined toothaxis and some reference data indicative of dimensions of the giventooth, the CR point thereon may be determined.

Non-limiting embodiments of the present technology may thus enable toaccurately determine the tooth axis based on image data of patient'sarch forms indicative solely of crown portions of the patient's teeth(such as that obtained using a conventional intraoral scanner, forexample), and not considering the root portions thereof, which may beexempt from obtaining additional image data associated with the patient,such as CT/magnetic resonance scans or a panoramic radiograph, forexample.

Accordingly, the non-limiting embodiments of the present technology aredirected to more efficient and effective methods and systems fordetermining the tooth axis, and further determining thereon the CR pointallowing for better predictability of the orthodontic treatmentplanning.

Therefore, according to a first broad aspect of the present technology,there is provided a method for determining a center of resistance pointof a tooth for orthodontic treatment planning. The method is executableby a processor. The method comprises: obtaining a tooth mesh from imagedata associated with a tooth crown of a patient, the tooth meshrepresentative of a surface of the tooth crown; identifying an internalreference point in the image data, the internal reference point being amesiodistal center of the tooth crown, the identifying the internalreference point comprising: obtaining a mesial point on a mesial side ofthe tooth crown, and a distal point on a distal side of the tooth crown;generating a mesiodistal line joining the mesial point and the distalpoint; identifying the mesiodistal center as a midpoint on themesiodistal line; determining a reference plane in the image data, thereference plane being perpendicular to the mesiodistal line andextending through the mesiodistal center; determining an intersectioncurve based on an intersection of the reference plane and the toothmesh, the intersection curve following a shape of the surface of thecrown at the reference plane; determining a tooth axis of the toothcrown based on the intersection curve; determining a crown height of thetooth crown based on the tooth axis; and determining the center ofresistance of the tooth based on the determined crown height and thedetermined tooth axis.

In some implementations of the method, the determining the tooth axis ofthe tooth crown based on the intersection curve comprises: bisecting theintersection curve into two intersection curve parts based on aseparation point; generating an average intersection curve using the twointersection curve parts; generating, based on the average intersectioncurve, a guide axis using a linear regression algorithm; and determiningthe tooth axis based on the guide axis.

In some implementations of the method, if the tooth is a premolar toothor a molar tooth, the separation point comprises: a point on theintersection curve which is closest to the internal reference point, andthe tooth axis is determined as the guide axis.

In some implementations of the method, if the tooth is an incisor toothor a canine tooth, the separation point comprises: for maxillary teeth,a minimum point of the intersection curve along a Z axis direction formaxillary teeth; and for mandibular teeth, a maximum point of theintersection curve in a Z axis direction for mandibular teeth.

In some implementations of the method, the determining the tooth axiscomprises: determining a linguolabial reference plane which is parallelto the mesiodistal line; dissecting the surface of the tooth crown, bythe linguolabial reference plane, into a lingual surface and a labialsurface; identifying lingual naked edges on the lingual surface of thesurface of the tooth crown; identifying labial naked edges on the labialsurface of the surface of the tooth crown; generating a lingual edgecurve based on projecting the lingual naked edges onto the linguolabialreference plane; generating a labial edge curve based on projecting thelabial naked edges onto the linguolabial reference plane; generating,based on the lingual edge curve and the labial edge curve, an averagelinguolabial edge curve; determining a linguolabial edge point, thedetermining comprises: for maxillary teeth, identifying a maximum pointof the linguolabial edge curve along a Y axis associated with thelinguolabial reference plane; and for mandibular teeth, identifying aminimum point of the linguolabial edge curve along the Y axis associatedwith the linguolabial reference plane; and determining the tooth axis byrotating the guide axis around Z axis associated with the linguolabialreference plane until it matches the linguolabial edge point on thelinguolabial plane.

In some implementations of the method, the determining the crown heightcomprises generating a bounding box around the tooth mesh and along thedetermined tooth axis, and determining the crown height as a height ofthe tooth mesh along the tooth axis.

In some implementations of the method, the determining the crown heightcomprises projecting tooth mesh vertices of the tooth mesh onto thetooth axis, and determining a distance difference between a minimumpoint and maximum point along the tooth axis.

In some implementations of the method, the method further comprisesmodulating the determined crown height by a predetermined distance.

In some implementations of the method, the determining the center ofresistance of the tooth based on the determined crown height and thedetermined tooth axis comprises: retrieving, from a memory, anapproximate root length based on the determined crown height; dividingthe approximate root length by two to define a center of resistancedistance; determining the center of resistance of the tooth as a pointalong the tooth axis at a distance relating to the center of resistancedistance from a crown start point.

In some implementations of the method, the image data is associated witha plurality of teeth crowns of the patient, and the determining thetooth mesh from the image data comprises determining a separate toothmesh for each one of the plurality of teeth crowns.

In some implementations of the method, the method further comprisesdisplaying the image data and one or both of the determined tooth axisand the determined center of resistance.

In some implementations of the method, the method further comprisesdetermining an orthodontic treatment using the determined center ofresistance.

According to a second broad aspect of the present technology, there isprovided a method for determining a center of resistance point of atooth for orthodontic treatment planning. The method is executable by aprocessor. The method comprises: receiving image data associated with atooth crown of a patient; determining a tooth mesh from the image data,the tooth mesh representative of a surface of the tooth crown;identifying an internal reference point in the image data, the internalreference point being based on a predetermined internal reference pointinstruction for locating the internal reference point in a given toothcrown; determining a reference plane in the image data, the referenceplane crossing the internal reference point and the tooth mesh and beingbased on a predetermined reference plane instruction for locating thereference plane relative to the internal reference point for a giventooth; determining an intersection curve based on an intersection of thereference plane and the tooth mesh, the intersection curve following ashape of the surface of the crown at the reference plane; determining atooth axis of the tooth crown based on the intersection curve;determining a crown height of the tooth crown based on the tooth axis;and determining the center of resistance of the tooth based on thedetermined crown height and the determined tooth axis.

In some implementations of the method, the internal reference pointcomprises a mesiodistal center of the tooth crown, the identifying theinternal reference point comprising: obtaining a mesial point on amesial side of the tooth crown, and a distal point on a distal side ofthe tooth crown, generating a mesiodistal line joining the mesial pointand the distal point; and identifying the mesiodistal center as amidpoint on the mesiodistal line.

In some implementations of the method, the reference plane isperpendicular to the mesiodistal line and extends through themesiodistal center.

In some implementations of the method, the determining the tooth axis ofthe tooth crown based on the intersection curve comprises: bisecting theintersection curve into two intersection curve parts based on aseparation point; generating an average intersection curve using the twointersection curve parts; generating, based on the average intersectioncurve, a guide axis using a linear regression algorithm; and determiningthe tooth axis based on the guide axis.

In some implementations of the method, if the tooth is a premolar toothor a molar tooth, the separation point comprises: a point on theintersection curve which is closest to the internal reference point, andthe tooth axis is determined as the guide axis; and if the tooth is anincisor tooth or a canine tooth, the separation point comprises: formaxillary teeth, a minimum point of the intersection curve along a Zaxis direction for maxillary teeth; and for mandibular teeth, a maximumpoint of the intersection curve in a Z axis direction for mandibularteeth.

In some implementations of the method, the determining the tooth axiscomprises: determining a linguolabial reference plane which is parallelto the mesiodistal line; dissecting the surface of the tooth crown, bythe linguolabial reference plane, into a lingual surface and a labialsurface; identifying lingual naked edges on the lingual surface of thesurface of the tooth crown; identifying labial naked edges on the labialsurface of the surface of the tooth crown; generating a lingual edgecurve based on projecting the lingual naked edges onto the linguolabialreference plane; generating a labial edge curve based on projecting thelabial naked edges onto the linguolabial reference plane; generating,based on the lingual edge curve and the labial edge curve, an averagelinguolabial edge curve; determining a linguolabial edge point, thedetermining comprises: for maxillary teeth, identifying a maximum pointof the linguolabial edge curve along a Y axis associated with thelinguolabial reference plane; and for mandibular teeth, identifying aminimum point of the linguolabial edge curve along the Y axis associatedwith the linguolabial reference plane; determining the tooth axis byrotating the guide axis around Z axis associated with the linguolabialreference plane until it matches the linguolabial edge point on thelinguolabial plane.

According to a third broad aspect of the present technology, there isprovided a system for determining a center of resistance point of atooth for orthodontic treatment planning. The system comprises aprocessor arranged to execute a method. The method comprises: receivingimage data associated with a tooth crown of a patient; determining atooth mesh from the image data, the tooth mesh representative of asurface of the tooth crown; identifying an internal reference point inthe image data, the internal reference point being based on apredetermined internal reference point instruction for locating theinternal reference point in a given tooth crown; determining a referenceplane in the image data, the reference plane crossing the internalreference point and the tooth mesh and being based on a predeterminedreference plane instruction for locating the reference plane relative tothe internal reference point for a given tooth; determining anintersection curve based on an intersection of the reference plane andthe tooth mesh, the intersection curve following a shape of the surfaceof the crown at the reference plane; determining a tooth axis of thetooth crown based on the intersection curve; determining a crown heightof the tooth crown based on the tooth axis; and determining the centerof resistance of the tooth based on the determined crown height and thedetermined tooth axis.

According to a fourth broad aspect of the present technology, there isprovided a system for determining a center of resistance point of atooth for orthodontic treatment planning. The system comprises aprocessor arranged to execute a method. The method comprises: obtaininga tooth mesh from image data associated with a tooth crown of a patient,the tooth mesh representative of a surface of the tooth crown;identifying an internal reference point in the image data, the internalreference point being a mesiodistal center of the tooth crown, theidentifying the internal reference point comprising: obtaining a mesialpoint on a mesial side of the tooth crown, and a distal point on adistal side of the tooth crown, generating a mesiodistal line joiningthe mesial point and the distal point; identifying the mesiodistalcenter as a midpoint on the mesiodistal line; determining a referenceplane in the image data, the reference plane being perpendicular to themesiodistal line and extending through the mesiodistal center;determining an intersection curve based on an intersection of thereference plane and the tooth mesh, the intersection curve following ashape of the surface of the crown at the reference plane; determining atooth axis of the tooth crown based on the intersection curve;determining a crown height of the tooth crown based on the tooth axis;and determining the center of resistance of the tooth based on thedetermined crown height and the determined tooth axis.

In the context of the present specification, unless expressly providedotherwise, a computer system may refer, but is not limited to, an“electronic device”, an “operation system”, a “system”, a“computer-based system”, a “controller unit”, a “control device” and/orany combination thereof appropriate to the relevant task at hand.

In the context of the present specification, unless expressly providedotherwise, the expression “computer-readable medium” and “memory” areintended to include media of any nature and kind whatsoever,non-limiting examples of which include RAM, ROM, disks (CD-ROMs, DVDs,floppy disks, hard disk drives, etc.), USB keys, flash memory cards,solid state-drives, and tape drives.

In the context of the present specification, a “database” is anystructured collection of data, irrespective of its particular structure,the database management software, or the computer hardware on which thedata is stored, implemented or otherwise rendered available for use. Adatabase may reside on the same hardware as the process that stores ormakes use of the information stored in the database or it may reside onseparate hardware, such as a dedicated server or plurality of servers.

In the context of the present specification, unless expressly providedotherwise, the words “first”, “second”, “third”, etc. have been used asadjectives only for the purpose of allowing for distinction between thenouns that they modify from one another, and not for the purpose ofdescribing any particular relationship between those nouns.

Embodiments of the present technology each have at least one of theabove-mentioned object and/or aspects, but do not necessarily have allof them. It should be understood that some aspects of the presenttechnology that have resulted from attempting to attain theabove-mentioned object may not satisfy this object and/or may satisfyother objects not specifically recited herein.

Additional and/or alternative features, aspects and advantages ofembodiments of the present technology will become apparent from thefollowing description, the accompanying drawings and the appendedclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the present technology, as well as otheraspects and further features thereof, reference is made to the followingdescription which is to be used in conjunction with the accompanyingdrawings, where:

FIG. 1 depicts a schematic diagram of an orthodontic appliance attachedto five teeth of a plurality of teeth of a subject;

FIG. 2 depicts a schematic diagram of an upper arch form of the subjectof FIG. 1 showing the orthodontic appliance of FIG. 1 attached thereto;

FIG. 3 depicts a schematic diagram of modelling uncontrolled tippingtooth movements of one of the plurality of teeth of the subject of FIG.1, in accordance with certain embodiments of the present technology;

FIG. 4 depicts a schematic diagram of modelling controlled tipping toothmovements of the one of the plurality of teeth of the subject of FIG. 1,in accordance with certain embodiments of the present technology;

FIG. 5 depicts a schematic diagram of modelling translational toothmovements of the one of the plurality of teeth of the patient of subjectof FIG. 1, in accordance with certain embodiments of the presenttechnology;

FIG. 6 depicts a schematic diagram of modelling root uprighting toothmovements of the one of the plurality of teeth of the subject of FIG. 1,in accordance with certain embodiments of the present technology;

FIG. 7 depicts a schematic diagram of a system for planning anorthodontic treatment for the subject of FIG. 1 based on determining acenter of resistance (CR) point for the one of the plurality of teethpresent in FIG. 1, in accordance with certain embodiments of the presenttechnology;

FIG. 8 depicts a schematic diagram of a computing environment of thesystem of FIG. 7, in accordance with certain embodiments of the presenttechnology;

FIG. 9 depicts a perspective view of a 3D model of the upper arch formand a lower arch form of the patient of FIG. 1, in accordance with thenon-limiting embodiments of the present technology;

FIG. 10 depicts respective distal views of a first 3D crown model and asecond 3D crown model of a crown portion associated with the one of theplurality of teeth present in FIG. 1 used by a processor of FIG. 8 fordetermining a tooth axis therefor, in accordance with the non-limitingembodiments of the present technology;

FIG. 11 depicts a perspective view of one of the first 3D crown modeland the second 3D crown model of FIG. 10 dissected by a mesiodistalplane for determining an intersection curve used by then processor ofFIG. 8 for determining the tooth axis for the one of the plurality ofteeth present in FIG. 1, in accordance with certain non-limitingembodiments of the present technology;

FIG. 12 depicts a cross-sectional mesiodistal view of the first 3D crownmodel of FIG. 10 used by the processor of FIG. 8 for determining a firstguide axis, thereby determining the tooth axis for the one of theplurality of teeth present in FIG. 1, in accordance with certainnon-limiting embodiments of the present technology;

FIG. 13 depicts a cross-sectional mesiodistal view of the second 3Dcrown model of FIG. 10 used by the processor of FIG. 8 for determining asecond guide axis, in accordance with certain non-limiting embodimentsof the present technology;

FIG. 14 depicts a labial view of the second 3D crown model of FIG. 10dissected by a linguolabial plane used by the processor of FIG. 8 fordetermining a linguolabial edge curve, in accordance with certainnon-limiting embodiments of the present technology;

FIG. 15 depicts a perspective view of the second 3D crown model of FIG.10 dissected by the linguolabial plane used by the processor of FIG. 8for determining a labial edge curve and a lingual edge curve, inaccordance with certain non-limiting embodiments of the presenttechnology;

FIG. 16 depicts a cross-sectional labial view of the second 3D crownmodel of FIG. 10 used by the processor of FIG. 10 for determining thelinguolabial edge curve, based on the lingual edge curve and the labialedge curve present in FIG. 15, and a respective linguolabial edge pointfor orienting the second guide axis of FIG. 13, thereby determining thetooth axis for the one of the plurality of teeth present in FIG. 1, inaccordance with certain non-limiting embodiments of the presenttechnology;

FIG. 17 depicts a schematic diagram of one of the first 3D crown modeland the second crown model of FIG. 10 enclosed in a bounding box used bythe processor of FIG. 8 for determining a crown portion height of thecrown portion associated with the one of the plurality of teeth presentin FIG. 1, in accordance with certain non-limiting embodiments of thepresent technology;

FIG. 18 depicts a cross-sectional mesiodistal view of one of the first3D crown model and the second 3D crown model of FIG. 10 used by theprocessor of FIG. 8 for determining a CR point for the one of theplurality of teeth present in FIG. 1 on the determined tooth axisassociated therewith, in accordance with certain non-limitingembodiments of the present technology;

FIG. 19 depicts a plurality of 3D crown models respectively associatedwith the plurality of teeth of the upper arch form present in FIG. 2used by the processor of FIG. 8 for planning the orthodontic treatment,in accordance with certain non-limiting embodiments of the presenttechnology;

FIG. 20 depicts a flowchart of a method for planning the orthodontictreatment for the subject of FIG. 1 based on the determined CR point, inaccordance with certain embodiments of the present technology.

DETAILED DESCRIPTION

Certain aspects and embodiments of the present technology are directedto methods of and systems for determining a center of resistance (CR)point for a given tooth of a patient receiving (or soon to receive) anorthodontic treatment. An accurate determination of the CR point mayfurther allow for a more accurate modelling of forces imposed on thegiven tooth in the course of the orthodontic treatment, which isbelieved to improve planning aspects thereof, such as expected efficacyand effectiveness in achieving respective treatment objectives(alignment of the given tooth, for example).

Further, it should be expressly understood that, in the context of thepresent specification, the term “orthodontic treatment” is broadlyreferred to as any type of medical intervention aimed at correctingmalocclusions associated with the patient, including surgical andnon-surgical manipulations, such as, but not limited to, using aligners.Further, the orthodontic treatment, as referred to herein, may bedetermined by a professional practitioner in the field of dentistry(such as an orthodontist, a maxillofacial surgeon, for example), orautomatically by a specific software, based on respective image data andinput parameters associated with the patient.

More specifically, certain aspects and embodiments of the presenttechnology comprise a computer-implemented method for determining atooth axis (also referred to herein as a “long axis”) for the giventooth represented by its crown portion; and further, determining the CRpoint on the tooth axis using certain reference data indicative ofdimensions of the given tooth.

Certain non-limiting embodiments of the present technology minimize,reduce or avoid some of the problems noted in association with the priorart. For example, by implementing certain embodiments of the presenttechnology in respect of determining the CR point for the given tooth,the following advantages may be obtained: a more efficient and accurateapproach to modelling movements of the given tooth during theorthodontic treatment. This is achieved in certain non-limitingembodiments of the present technology by determining the tooth axis forthe given tooth using image data only of the crown portion thereof,without the need for considering the root portion thereof, which wouldrequire obtaining and processing additional image data associated withthe patient, such as CT and/or magnetic resonance scans or panoramicradiographs, for example. In this regard, methods and systems providedherein, according to certain non-limiting embodiments of the presenttechnology, allow achieving a higher accuracy in planning andpredictability of orthodontic treatments, and consequently, resolvingmalocclusions more efficiently and effectively whilst minimizing theimage data to be obtained from the patient and processed by a processor.

Biomechanics of Tooth Movements

Referring initially to FIGS. 1 and 2, there is depicted an exampleorthodontic appliance 10 as part of the orthodontic treatment, to whichaspects and embodiments of the present technology can be applied.Generally speaking, the orthodontic appliance 10 comprises brackets 12and an archwire 14. The archwire 14 is made of a shape memory alloy suchas Nitinol™, but can also be made of any other shape memory alloy ormaterial having certain elasticity properties. The brackets 12 arerespectively provided on some of upper teeth 16 (depicted individuallyas 16 a, 16 b, 16 c, 16 d, and 16 e), and the archwire 14 extendsbetween, and is connected to, each of the brackets 12. In the depictedembodiments of FIG. 1, the orthodontic treatment is aimed atmisalignment of the tooth 16 c; hence the orthodontic appliance 10 isconfigured to cause the tooth 16 c to move in a predetermined direction(such as downwardly) for alignment thereof with neighbouring ones of theupper teeth 16, that is teeth 16 a, 16 b, 16 d, and 16 e.

As it can be appreciated, the archwire 14 of FIG. 1 has bends 18, whichwill gradually move towards an aligned position when installed in amouth of a subject (also referred to herein as a “patient”, notdepicted) due to the shape memory effect of the archwire 14, whichimposes a given force on the tooth 16 c at a respective one of thebrackets 12 of the orthodontic appliance 10.

With reference to FIG. 2, as one non-limiting example, the orthodonticappliance 10 has been applied to all the upper teeth 16 of an upper archform 20 of the subject, with the brackets 12 being attached to aninternal surface 22 of the upper teeth 16. However, it should be notedthat, in another non-limiting example, the orthodontic appliance 10 maybe configured to be installed on an external surface 24 of the upperteeth 16.

It is contemplated that, according to some non-limiting embodiments ofthe present technology, the orthodontic appliance 10 may compriseorthodontic appliances of different types, shapes, sizes andconfigurations, such as, without limitation, multi-strand wires, strips,retainers, and plates. Furthermore, the bends 18 in the archwire 14 maycomprise rounded corners or loops. It will also be appreciated that theorthodontic appliance 10 may be used for treating any type of teethmisalignment or malocclusion, including but not limited to closing gaps(“space closure”), creating/widening gaps, tooth rotation, toothintrusion/extrusion, and translation, to name a few.

However, before applying the given force on the tooth 16 c, a magnitudeand a direction thereof should be accurately calculated, therebymodelling the respective movements of the tooth 16 c, to ensure thetooth 16 c, during the orthodontic treatment, will be moving towards thealigned position.

More specifically, according to some non-limiting embodiments of thepresent technology, the modelling of the movements of the tooth 16 cunder the given force may be implemented based on determining a positionof a line of action of the given force relative to a center ofresistance (CR) point of the tooth 16 c.

In the context of the present specification, the term “CR point” of agiven body is broadly referred to as a point, at which imposing a givenmechanical force results in a translational movement (or otherwise, abodily movement) of the given body in a direction of the givenmechanical force, along a line of action thereof. As used herein, the CRpoint is mostly determined for restrained bodies, such as teeth (forexample, the tooth 16 c), and, in a sense, may be considered as anequivalent to a center of gravity point (center of mass point) forunrestrained (free) bodies.

Further, the non-limiting embodiments of the present technology havebeen developed based on a premise that the CR point for the tooth 16 c(such as a CR point 40 depicted in FIG. 3) can typically be found on atooth axis associated therewith (such as a tooth axis 42). In thecontext of the present specification, the term “tooth axis” of the giventooth is referred to as a line extending through the given toothlengthwise, through a crown portion and a root portion thereof, aroundwhich mass of the given tooth as well as anatomical features (such aslobes, developmental grooves, and marginal ridges thereof, for example)thereof are distributed substantially symmetrically.

With reference to FIG. 3, there is depicted a schematic diagram of adistal view of the tooth 16 c illustrating an example of modelledmovements from a force 32 applied thereon, in accordance with certainnon-limiting embodiments of the present technology.

As it can be appreciated, the tooth 16 c includes a crown portion 26 anda root portion 28. Tissues of a periodontium 30 surrounding andsupporting the upper teeth 16, and the tooth 16 c, in particular,include a gingiva 34, an alveolar bone 36, and a periodontal ligament38. The periodontal ligament 38 surrounds the root portion 26 andattaches the tooth 16 c to the alveolar bone 36. Thus, it can be saidthat the tooth 16 c is restrained in the alveolar bone 36 by forces (notseparately depicted) from the periodontal ligament 38 and theneighboring upper teeth 16 (depicted in FIGS. 1 and 2). As such, alocation of the CR point 40 on the tooth axis 42 may vary depending on anumber of roots of the tooth 16 c, a length of the root portion 28, anda level (height) of the alveolar bone 36.

Thus, for example, it may be shown that in certain subjects the CR point40 can be determined to be located on the tooth axis 42 at a length from24 to 35% of a length of the root portion 28 apically (towards an apex44 of the tooth 16 c) from an alveolar crest 46 of the alveolar bone 36.

Accordingly, using a bracket 12 c of the brackets 12 installed on thecrown portion 26, the force 32 may be imposed on the tooth 16 c.Consequently, under the force 32, the tooth 16 c deforming theperiodontal ligament 38 may move towards the aligned position. Aspreviously noted, the dynamics of the movements of the tooth 16 c, as itmoves towards the aligned position, can be said to be defined by thedirection and the magnitude of the force 32. To that end, the directionand the magnitude of the force 32 imposed on the tooth 16 c may bedetermined by a particular configuration of the orthodontic appliance 10and components thereof, that is, the brackets 12 and the archwire 14,which includes, without being limited to, a material of the archwire 14and elasticity properties associated therewith, a thickness of thearchwire 14, a configuration of a given one of the brackets 12 defininga method for installing the archwire 14 therein, and the like. Further,it should be expressly understood that the force 32 is depicted in FIG.3 as a single force only for the sake of clarity of the presentdescription, and may comprise a superposition of a system of forcesapplied to the tooth 16 c at the bracket 12 c as well as at othercomponents (not separately depicted) of the orthodontic appliance 10installed thereon such as springs, ligatures, coils, anchors, and thelike.

Further, as the force 32 is applied to the crown portion 26 with a lineof action 33 thereof not extending through the CR point 40, it maytypically create a torque 48. Accordingly, such an application of theforce 32 may cause the tooth 16 c to move (1) translationally, as if theforce 32 is applied to the CR point 40; and (2) rotationally around acenter of rotation 50. It should be noted that, akin to the force 32,the torque 48 may be a resultant force torque of a torque systeminfluencing the tooth 16 c caused by the force 32. In this regard, thetorque 48 may be determined in accordance with the following equation:T=F×D,  (1)where T is the torque 48,

-   -   F is the force 32, and    -   D is a distance 52, over a perpendicular, between the CR point        40 and the line of action 33.

Practically speaking, a particular movement of the tooth 16 c may beprojected by varying a torque-to-force ratio T:F between the torque 48and the force 32. To that end, as it can be appreciated from Equation(1), after applying the force 32 of a given magnitude, a magnitude ofthe torque 48 may be varied by varying the distance 52 from the line ofaction 33 to the CR point 40. Thus, the longer the distance 52, thehigher the torque-to-force ratio T:F.

Thus, in one non-limiting example, in certain subjects, when the ratioT:F is 0:1, the tooth 16 c will move purely rotationally with the centerof rotation 50 substantially coinciding with the CR point 40. To thatend, the crown portion 26 will be moving labially (buccally) and theapex 44 will be moving lingually. Such a movement can also be referredto as an uncontrolled tipping tooth movement.

With reference to FIG. 4, there is depicted a schematic diagram of thedistal view of the tooth 16 c illustrating another example of modelledmovements from the force 32 applied thereon, in accordance with somenon-limiting embodiments of the present technology.

In the depicted embodiments of FIG. 4, the torque-to-force ratio T:F isbetween 5:1 and 7:1, which causes the center of rotation 50 to shifttowards the apex 44, in certain subjects. To that end, the force 32causes the tooth 16 c to move as a “pendulum” around the apex 44. Byvarying the ratio T:F within a predetermined range, it is possible toproduce similar movements of the tooth 16 c based on respectivelocations of the center of rotation 50 near the apex 44, each of thesemovements can be referred to as a controlled tipping tooth movement.

With reference to FIG. 5, there is depicted a schematic diagram of thedistal view of the tooth 16 c illustrating yet another example ofmodelled movements from the force 32 applied thereon, in accordance withsome non-limiting embodiments of the present technology.

In the depicted embodiments of FIG. 5, the torque-to-force ratio T:F isaround 10:1, which causes the center of rotation 50 to shift toinfinity. Accordingly, with such a value of the torque-to-force ratioT:F, the torque 48 can be said to cause the line of action 33 of theforce 32 to extend through the CR point 40, thereby causing the tooth 16c, in certain subjects, to move purely translationally therealong. Suchmovements can also be referred to as bodily tooth movements.

Some non-limiting examples of the bodily tooth movements of the tooth 16c may also include an extrusion tooth movement and an intrusion toothmovement (not separately depicted) where the force 32 is directed alongthe tooth axis 42 through the CR point 40 downwards or upwards,respectively.

Finally, with reference to FIG. 6, there is depicted a schematic diagramof the distal view of the tooth 16 c illustrating yet another example ofmodelled movements from the force 32 applied thereon, in accordance withsome non-limiting embodiments of the present technology.

As it can be appreciated, when the torque-to-force ratio T:F is furtherincreased to values such as 14:1, for example, the center or rotation 50may be shifted to the crown portion 26, thereby causing the tooth 16 cto rotate around the crown portion 26. To that end, the apex 44 of theroot portion 28 moves buccally, which can be referred to as a rootuprighting tooth movement.

Thus, it is contemplated that, based on a current position of the toothaxis 42 relative to the crown portion 26, respective values of the force32 and the torque 48 needed to cause the tooth 16 c to move towards thealigned position may be determined. Further, in those embodiments of thepresent technology where the orthodontic treatment for the subject isgenerated based on image data associated only with the crown portion 26,the tooth axis 42 may be used to determine a position of the rootportion 28 relative to the crown portion 26.

As it can be apparent from the description above, at least some of theso modelled tooth movements may be used to plan the orthodontictreatment for the subject to cause the tooth 16 c to move towards thealigned position. Accordingly, an accurate determination of the toothaxis 42 and the CR point 40 thereon may further allow for a moreaccurate planning of the orthodontic treatment for the subject aimed atmitigating the probability of discrepancies between planned toothmovements and actual tooth movements in the course of the orthodontictreatment. How the tooth axis 42 and the CR point 40 can be determinedfor the tooth 16 c, in accordance with the non-limiting embodiments ofthe present technology, will be described below with reference to FIGS.9 to 18.

System

Now, with reference to FIGS. 7 to 8, there is depicted a schematicdiagram of a system 700 suitable for determining the tooth axis 42 andfurther the CR point 40 thereon, in accordance with some non-limitingembodiments of the present technology.

It is to be expressly understood that the system 700 as depicted ismerely an illustrative implementation of the present technology. Thus,the description thereof that follows is intended to be only adescription of illustrative examples of the present technology. Thisdescription is not intended to define the scope or set forth the boundsof the present technology. In some cases, what is believed to be helpfulexamples of modifications to the system 700 may also be set forth below.This is done merely as an aid to understanding, and, again, not todefine the scope or set forth the bounds of the present technology.These modifications are not an exhaustive list, and, as a person skilledin the art would understand, other modifications are likely possible.Further, where this has not been done (i.e., where no examples ofmodifications have been set forth), it should not be interpreted that nomodifications are possible and/or that what is described is the solemanner of implementing that element of the present technology. As aperson skilled in the art would understand, this is likely not the case.In addition, it is to be understood that the system 700 may provide incertain instances simple implementations of the present technology, andthat where such is the case they have been presented in this manner asan aid to understanding. As persons skilled in the art would understand,various implementations of the present technology may be of a greatercomplexity.

In certain non-limiting embodiments of the present technology, thesystem 700 of FIG. 7 comprises a computer system 710. The computersystem 710 is configured, by pre-stored program instructions, todetermine the tooth axis 42 and further the CR point 40 thereon, basedon image data associated with the subject, according to the non-limitingembodiments of the present technology.

To that end, in some non-limiting embodiments of the present technology,the computer system 710 is configured to receive image data pertainingto the subject or to a given orthodontic treatment. The computer system710 may use the image data for determining the tooth axis 42. Accordingto some non-limiting embodiments of the present technology, the computersystem 710 may receive the image data via local input/output interface(such as USB, as an example, not separately depicted). In othernon-limiting embodiments of the present technology, the computer system710 may be configured to receive the image data over a communicationnetwork 725, to which the computer system 710 is communicativelycoupled.

In some non-limiting embodiments of the present technology, thecommunication network 725 is the Internet and/or an Intranet. Multipleembodiments of the communication network may be envisioned and willbecome apparent to the person skilled in the art of the presenttechnology. Further, how a communication link between the computersystem 710 and the communication network 725 is implemented will depend,inter alia, on how the computer system 710 is implemented, and mayinclude, but is not limited to, a wire-based communication link and awireless communication link (such as a Wi-Fi communication network link,a 3G/4G communication network link, and the like).

It should be noted that the computer system 710 can be configured forreceiving the image data from a vast range of devices. Some such devicescan be used for capturing and/or processing data pertaining tomaxillofacial and/or cranial anatomy of a subject. In certainembodiments, the image data received from such devices is indicative ofproperties of anatomical structures of the subject, including: teeth,intraoral mucosa, maxilla, mandible, temporomandibular joint, and nervepathways, among other structures. In some embodiments, at least some ofthe image data is indicative of properties of external portions of theanatomical structures, for example dimensions of a gingival sulcus, anddimensions of an external portion of a tooth (e.g., a crown of thetooth) extending outwardly of the gingival sulcus. In some embodiments,the image data is indicative of properties of internal portions of theanatomical structures, for example volumetric properties of bonesurrounding an internal portion of the tooth (e.g., a root of the tooth)extending inwardly of the gingival sulcus. Under certain circumstances,such volumetric properties may be indicative of periodontal anomalieswhich may be factored into an orthodontic treatment plan. In somenon-limiting embodiments of the present technology, the image dataincludes cephalometric image datasets. In some embodiments, the imagedata includes datasets generally intended for the practice ofendodontics. In some embodiments, the image data includes datasetsgenerally intended for the practice of periodontics.

The image data may include two-dimensional (2D) data and/orthree-dimensional data (3D). In certain embodiments, the image dataincludes at least one dataset derived from one or more of the followingimaging modalities: computed tomography (CT), radiography, magneticresonance imaging, ultrasound imaging, nuclear imaging and opticalimaging. Any medical imaging modality is included within the scope ofthe present technology. In certain non-limiting embodiments of thepresent technology, the image data includes 2D data, from which 3D datamay be derived, and vice versa.

In alternative non-limiting embodiments of the present technology, thecomputer system 710 may be configured to receive the image dataassociated with the subject directly from an imaging device 730communicatively coupled thereto. Broadly speaking the imaging device 730may be configured (for example, by a processor 850 depicted in FIG. 8)to capture and/or process the image data of the upper teeth 16 and theperiodontium 30 of the subject. In certain non-limiting embodiments ofthe present technology, the image data may include, for example, one ormore of: (1) images of external surfaces of respective crown portions(such as the crown portion 26 of the tooth 16 c) of the upper teeth 16,(2) images of an external surface of the periodontium 30 including thoseof the gingiva 34, the alveolar bone 36, and images of blood vessels andnerve pathways associated with the upper teeth 16; and (3) images of anoral region. By doing so, the imaging device 730 may be configured, forexample, to capture image data of the upper arch form 20 of the subject.In another example, the imaging device may also be configured to captureand/or process image data of a lower arch form (such as the lower archform 21 depicted in FIG. 9) associated with the subject withoutdeparting from the scope of the present technology.

In some non-limiting embodiments of the present technology, the imagingdevice 730 may comprise an intra-oral scanner enabling to capture directoptical impressions of the upper arch form 20 of the subject.

In a specific non-limiting example, the intraoral scanner can be of oneof the types available from MEDIT, corp. of 23 Goryeodae-ro 22-gil,Seongbuk-gu, Seoul, Korea. It should be expressly understood that theintraoral scanner can be implemented in any other suitable equipment.

In other non-limiting embodiments of the present technology, the imagingdevice 730 may comprise a desktop scanner enabling to digitize a moldrepresenting the upper arch form 20. In this regard, the mold may havebeen obtained via dental impression using a material (such as a polymer,e.g. polyvinyl-siloxane) having been imprinted with the shape of theintraoral anatomy it has been applied to. In the dental impression, aflowable mixture (i.e., dental stone powder mixed with a liquid incertain proportions) may be flowed such that it may, once dried andhardened, form the replica.

In a specific non-limiting example, the desktop scanner can be of one ofthe types available from Dental Wings, Inc. of 2251, ave Letourneux,Montréal (QC), Canada, H1V 2N9. It should be expressly understood thatthe desktop scanner can be implemented in any other suitable equipment.

Further, it is contemplated that the computer system 710 may beconfigured for processing of the received image data. The resultingimage data of the upper teeth 16 received by the computer system 710 istypically structured as a binary file or an ASCII file, may bediscretized in various ways (e.g., point clouds, polygonal meshes,pixels, voxels, implicitly defined geometric shapes), and may beformatted in a vast range of file formats (e.g., STL, OBJ, PLY, DICOM,and various software-specific, proprietary formats). Any image data fileformat is included within the scope of the present technology. Forimplementing functions described above, the computer system 710 mayfurther comprise a corresponding computing environment.

With reference to FIG. 8, there is depicted a schematic diagram of acomputing environment 840 suitable for use with some implementations ofthe present technology. The computing environment 840 comprises varioushardware components including one or more single or multi-coreprocessors collectively represented by the processor 850, a solid-statedrive 860, a random access memory 870 and an input/output interface 880.Communication between the various components of the computingenvironment 840 may be enabled by one or more internal and/or externalbuses 890 (e.g. a PCI bus, universal serial bus, IEEE 1394 “Firewire”bus, SCSI bus, Serial-ATA bus, ARINC bus, etc.), to which the varioushardware components are electronically coupled.

The input/output interface 880 allows enabling networking capabilitiessuch as wire or wireless access. As an example, the input/outputinterface 880 comprises a networking interface such as, but not limitedto, a network port, a network socket, a network interface controller andthe like. Multiple examples of how the networking interface may beimplemented will become apparent to the person skilled in the art of thepresent technology. For example, but without being limiting, theinput/output interface 880 may implement specific physical layer anddata link layer standard such as Ethernet™, Fibre Channel, Wi-Fi™ orToken Ring. The specific physical layer and the data link layer mayprovide a base for a full network protocol stack, allowing communicationamong small groups of computers on the same local area network (LAN) andlarge-scale network communications through routable protocols, such asInternet Protocol (IP).

According to implementations of the present technology, the solid-statedrive 860 stores program instructions suitable for being loaded into therandom access memory 870 and executed by the processor 850, according tocertain aspects and embodiments of the present technology. For example,the program instructions may be part of a library or an application.

In these embodiments, the computing environment 840 is implemented in ageneric computer system which is a conventional computer (i.e. an “offthe shelf” generic computer system). The generic computer system may bea desktop computer/personal computer, but may also be any other type ofelectronic device such as, but not limited to, a laptop, a mobiledevice, a smart phone, a tablet device, or a server.

As persons skilled in the art of the present technology may appreciate,multiple variations as to how the computing environment 840 isimplemented may be envisioned without departing from the scope of thepresent technology.

Referring back to FIG. 7, the computer system 710 has at least oneinterface device 720 for providing an input or an output to a user ofthe system 700, the interface device 720 being in communication with theinput/output interface 880. In the embodiment of FIG. 7, the interfacedevice is a screen 722. In other non-limiting embodiments of the presenttechnology, the interface device 720 may be a monitor, a speaker, aprinter or any other device for providing an output in any form such asimage-form, written form, printed form, verbal form, 3D model form, orthe like.

In the depicted embodiments of FIG. 7, the interface device 720 alsocomprises a keyboard 724 and a mouse 726 for receiving input from theuser of the system 700. Other interface devices 720 for providing aninput to the computer system 710 can include, without limitation, a USBport, a microphone, a camera or the like.

The computer system 710 may be connected to other users, such as throughtheir respective clinics, through a server (not depicted). The computersystem 710 may also be connected to stock management or client softwarewhich could be updated with stock when the orthodontic treatment hasbeen determined and/or schedule appointments or follow-ups with clients,for example.

Image Data

As previously alluded to, according to the non-limiting embodiments ofthe present technology, the processor 850 may be configured to: (1)receive the image data associated with the subject's teeth (such as theupper teeth 16); (2) based on the received image data, determine, foreach of the upper teeth 16, a respective tooth axis (such as the toothaxis 42 of the tooth 16 c); and (3) determine a respective CR point oneach of the tooth axes (such the CR point 40).

According to some non-limiting embodiments of the present technology,the processor 850 may be configured to receive 3D models of arch formsof the subject.

With reference to FIG. 9, there is depicted a perspective view of a 3Dmodel 900 representing a current configuration of the upper arch form 20(also referred to herein as “maxillary arch form”) and the lower archform 21 (also referred to herein as “mandibular arch form”) of thesubject, in accordance with the non-limiting embodiments of the presenttechnology.

According to the non-limiting embodiments of the present technology, theupper arch form 20 comprises the upper teeth 16 (also referred to hereinas “maxillary teeth”) and the gingiva 36, and the lower arch form 21comprises lower teeth 17 (also referred to herein as “mandibular teeth”)and lower gingiva 37. As it can be appreciated, the upper teeth 16 andthe lower teeth 17 are represented, in the 3D model 900, by respectivecrown portions associated therewith.

In some non-limiting embodiments of the present technology, afterreceiving the 3D model 900, the processor 850 may be configured tosegment thereon crown portions associated with the respective teeth fromeach other as well as from an associated gingiva, thereby generating aplurality of so segmented crown portions associated with one of theupper arch form 20 and the lower arch form 21 of the subject. To thatend, according to some non-limiting embodiments of the presenttechnology, the processor 850 may be configured to apply one or moreapproaches to automatic tooth segmentation, for example, one, which isdescribed in a co-owned U.S. patent application Ser. No. 16/703,471,entitled “METHOD AND SYSTEM FOR DENTAL BOUNDARY DETERMINATION”, thecontent of which is hereby incorporated by reference in its entirety.

Although the description below will be given in respect of the upperteeth 16 for the sake of clarity and simplicity thereof, and in no wayas a limitation, it should be expressly understood that the non-limitingembodiments of the present technology may also apply to the lower teeth17 with certain alterations, which will be explicitly indicated belowwhere necessary.

Thus, for example, the processor 850 may be configured to generate a 3Dcrown model for a given one of the upper teeth 16 (such as the crownportion 26 of the tooth 16 c) representative of a surface thereof.

The non-limiting embodiments of the present technology have beendeveloped based on a premise that the upper teeth 16 should beconsidered in certain groups, into which they may be divided based oncommon parameters associated therewith. These parameters may includecertain surface features of an associated crown portion (such ascurvature in a distal projection, for example) and anatomical features(such as a number of cusps of an associated crown portion or a number ofroots in an associated root portion) of the given one of the upper teeth16. In this regard, the developers have realized that the determinationof a given tooth axis for premolars and molars can be different fromthat for incisors and canines, thereby dividing the upper teeth 16 intoa first group and a second group, respectively.

Thus, depending on which of the first group or the second group thetooth 16 c is associated with, the processor 850 can be configured togenerate different 3D crown models of the crown portion 26.

With reference to FIG. 10, there is depicted a distal view of a first 3Dcrown model 1002 of the crown portion 26; and a second 3D crown model1004 of the crown portion 26, in accordance with certain non-limitingembodiments of the present technology. Each of the first 3D crown model1002 and the second 3D crown model 1004 has been segmented, by theprocessor, from the 3D model 900.

Thus, the description below will be provided in light of two scenarios:in Scenario 1, there will be described implementations of certainnon-limiting embodiments of the present technology in respect of thefirst 3D crown model 1002; whereas in Scenario 2, there will bedescribed those in respect of the second 3D crown model 1004.

Determining Crown Curvature

According to the non-limiting embodiments of the present technology, theprocessor 850 may be configured to determine the tooth axis 42 based onanalyzing certain aspects of crown curvature of the crown portion 26. Tothat end, the processor 850 may be configured to determine anintersection curve of one of the first 3D crown model 1002 and thesecond 3D crown model 1004 with a mesiodistal plane. This sectionequally applies to both Scenario 1 and Scenario 2.

With reference to FIG. 11, there is depicted a perspective view of thefirst 3D crown model 1002 dissected by a first mesiodistal plane 1110,according to some non-limiting embodiments of the present technology.

First, according to the non-limiting embodiments of the presenttechnology, the processor 850 may be configured to identify a distalpoint 1102 and a mesial point 1104 on the 3D crown model 1002.

In some non-limiting embodiments of the present technology, theprocessor 850 may be configured to identify each of the distal point1102 and the mesial point 1104 as being highest curvature points on adistal surface and a mesial surface of the first 3D crown model 1002,respectively. In other words, the processor 850 may be configured toidentify each of the distal point 1102 and the mesial point 1104 to beindicative of those lying within a contact region (not separatelydepicted) between the crown portion 26 and crown portions of adjacentones of the upper teeth 16. To that end, in some non-limitingembodiments of the present technology, each of the distal point 1102 andthe mesial point 1104 may be identified outside the first 3D crown model1002.

Further, according to the non-limiting embodiments of the presenttechnology, the processor 850 may be configured to join the distal point1102 and the mesial point 1104, thereby generating a mesiodistal line1106 associated with the first 3D crown model 1002. The processor 850may further be configured to determine, on the mesiodistal line 1106, areference point 1108 for determining the mesiodistal plane 1110 inaccordance with a predetermined rule. For example, the processor 850 maybe configured to determine the reference point 1108 based on a positionalong the mesiodistal line 1106 according to a predetermined ratiobetween the distal surface and the mesial surface (such as 1:3 or 1:5,for example). In another example, the processor 850 may be configured todetermine the reference point 1108 as a projection of certain anatomicalspecifics of the crown portion 26 indicated by the first 3D crown model1002, such as cusps or grooves, onto the mesiodistal line 1106.

In specific non-limiting embodiments of the present technology, theprocessor 850 may be configured to determine the reference point 1108 asa midpoint of the mesiodistal line 1106, which may be referred to hereinas a “mesiodistal center” associated with the first 3D crown model 1002.

According to some non-limiting embodiments of the present technology,based on the reference point 1108, the processor 850 may be configuredto determine a coordinate system 1105 for the first 3D crown model 1002assigning its center to the reference point 1108 with a Z axis beingperpendicular to the mesiodistal line 1106 and directed upwards. As itcan be appreciated, for a 3D crown model of a respective one of thelower teeth 17, an associated Z axis would be directed downwardly.

Further, as it can be appreciated, a Y axis of the coordinate system1105 may be parallel to the mesiodistal line 1106; and an X axis of thecoordinate system 1105 may hence be perpendicular to the mesiodistalline 1106.

Further, the processor 850 may be configured to construct the firstmesiodistal plane 1110 to originate in the reference point 1108 and tobe perpendicular to the mesiodistal line 1106. Accordingly, in somenon-limiting embodiments of the present technology, by doing so, theprocessor 850 is configured to determine a first intersection curve 1112between the first 3D crown model 1002 and the first mesiodistal plane1110.

Generating Guide Axis

According to the non-limiting embodiments of the present technology, theprocessor 850 may further be configured to generate a so-called guideaxis, based on the first intersection curve 1112, for furtherdetermining the tooth axis 42.

Scenario 1

With reference to FIG. 12, there is depicted a schematic diagram of across-sectional mesiodistal view of the first 3D crown model 1002produced by the first mesiodistal plane 1110 for generating a firstguide axis 1202 associated therewith, according to some non-limitingembodiments of the present technology.

According to some non-limiting embodiments of the present technology,the processor 850 may be configured to generate the first guide axis1202 based on certain segments of the first intersection curve 1112. Tothat end, first, the processor 850 may be configured to determine afirst separation point 1204 for segmenting the first intersection curve1112.

According to some non-limiting embodiments of the present technology,the processor 850 may be configured to identify the first separationpoint 1204 as a point of the first intersection curve 1112, which isclosest, within the coordinate system 1105, to the reference point 1108associated with the first 3D crown model 1002. In other words, the firstseparation point 1204 may be determined as a point of a highest positivecurvature of the first intersection curve 1112. In other non-limitingembodiments of the present technology, the processor 850 may beconfigured to identify the first separation point 1204 as a median pointof the first intersection curve 1112, as an example.

Thus, using the first separation point 1204, the processor 850 may beconfigured to segment the first intersection curve 1112 into at least afirst subcurve 1206 and a second subcurve 1208. Further, the processor850 may be configured to generate, based on the first subcurve 1206 andthe second subcurve 1208, a first average intersection curve 1210. Tothat end, according to some non-limiting embodiments of the presenttechnology, the processor 850 may be configured to use one or more curvefitting techniques, which may include, without being limited to, one ormore of: a linear curve fitting technique, a non-linear curve fittingtechnique, including, for example, a polynomial curve fitting technique,an exponential curve fitting technique, a logarithmic curve fittingtechnique, a spline curve fitting technique, and the like.

Further, according to some non-limiting embodiments of the presenttechnology, the processor 850 may be configured to generate the firstguide axis 1202 by linearly approximating the first average intersectioncurve 1210. To that end, the processor 850 may be configured to applyone or more linear curve fitting techniques. Accordingly, in somenon-limiting embodiments of the present technology, the first separationpoint 1204 may lie on the first guide axis 1202.

In specific non-limiting embodiments of the present technology, theapplying one or more linear fitting technique may include applying alinear regression algorithm to the average intersection curve 1210.

Scenario 2

With reference to FIG. 13, there is depicted a cross-sectionalmesiodistal view of the second 3D crown model 1004 produced by a secondmesiodistal plane 1320 for determining a second guide axis 1302associated therewith, according to some non-limiting embodiments of thepresent technology.

As it may become apparent, the processor 850 may have been configured todetermine a second reference point 1308, thereby allocating a secondcoordinate system 1107 for the second 3D crown model 1004 similar towhat is described in respect of the reference point 1108 and thecoordinate system 1105, respectively. It should be expressly understoodthat although, generally speaking, the coordinate system 1105 and thesecond coordinate system 1107 are different, and include differentrelative angular orientations of associated axes; in some non-limitingembodiments of the present technology, their Z-axes may have the sameangular orientation.

Further, the processor 850 may have been configured to generate thesecond mesiodistal plane 1320, based on the second reference point 1308,thereby forming a second intersection curve 1312, in a similar fashionto that used for generating the first intersection curve 1112.

According to some non-limiting embodiments of the present technology,the processor 850 may be configured to determine a second separationpoint 1304 as a minimum point of the second intersection curve 1312along a Z axis of the second coordinate system 1107 associated with thesecond 3D crown model 1004. As it may further become apparent, aseparation point associated with a 3D crown model (not separatelydepicted) of the respective one of the lower teeth 17 may be identified,by the processor 850, as a maximum point of an associated intersectioncurve along a Z axis within an associated coordinate system.

Further, according to some non-limiting embodiments of the presenttechnology, using the second separation point 1304, the processor 850may be configured to segment the second intersection curve 1312 forgenerating a second average intersection curve 1310, and based thereon,generating the second guide axis 1302 in a similar fashion to thatdescribed above in respect of the first guide axis 1202 in Scenario 1.

Determining Tooth Axis

As previously mentioned, based on one of the first guide axis 1202 andthe second guide axis 1302, the processor 850 may further be configuredto determine the tooth axis 42 associated with the tooth 16 c.

Scenario 1

According to some non-limiting embodiments of the present technology,the first guide axis 1202 may define the tooth axis 42 of the tooth 16c.

Thus, it can be said that the processor 850 may be configured todetermine the tooth axis 42 of the tooth 16 c, based on the first 3Dcrown model 1002 of the crown portion 26, as a line having beengenerated based on the first intersection curve 1112 and extendingthrough the first separation point 1204.

Scenario 2

According to some non-limiting embodiments of the present technology,the processor 850 may be configured to determine the tooth axis 42 bydetermining an angular orientation for the second guide axis 1302 in alinguolabial plane associated with the second 3D crown model 1004.

With reference to FIG. 14, there is depicted a labial view of the second3D crown model 1004 dissected by a linguolabial plane 1410, inaccordance with some non-limiting embodiments of the present technology.

As it can be appreciated from FIG. 14, the processor 850 may have beenconfigured to identify a second distal point 1402 and a second mesialpoint 1404 for the second 3D crown model 1004 in a way similar to thatdescribed above in respect of the distal point 1102 and the mesial point1104. Further, by joining the second distal point 1402 and the secondmesial point 1404, the processor 850 may have been configured togenerate a second mesiodistal line 1406, and further to generate thereonthe second reference point 1308 using one of the respective approachesdescribed above.

According to some non-limiting embodiments of the present technology,the processor 850 may be configured to generate the linguolabial plane1410 to be parallel to the second mesiodistal line 1406. In othernon-limiting embodiments of the present technology, the processor 850may be configured to generate the linguolabial plane 1410 to be parallelto the second mesiodistal line 1406 and perpendicular to the secondmesiodistal plane 1320 (as depicted in FIG. 13).

Thus, by determining a point in the linguolabial plane 1410 to be usedfor directing the second guide axis 1302 from the second separationpoint 1304, the processor 850 may further be configured to determine thetooth axis 42. In this regard, according to some non-limitingembodiments of the present technology, the processor 850 may beconfigured to determine a linguolabial edge curve associated with thesecond 3D crown model 1004.

With reference to FIGS. 15 and 16, there is depicted a perspective viewof the second 3D crown model 1004 dissected by the linguolabial plane1410 and a cross-sectional labial view thereof produced by thelinguolabial plane 1410, respectively, for determining a linguolabialedge curve 1606, in accordance with certain non-limiting embodiments ofthe present technology.

According to some non-limiting embodiments of the present technology,the processor 850 may be configured to determine the linguolabial edgecurve 1606 based on projecting so-called naked edges of each one of alabial surface 1502 and a lingual surface 1504 of the second 3D crownmodel 1004 onto the linguolabial plane 1410.

In the context of the present specification, the term “naked edge”relates to mesh representation techniques of objects (such as usingtriangle meshes, for example) and is referred to as an edge of a givenmesh element of a given mesh representation associated with an objectsurface that forms only that given mesh element without being joined toany other mesh element of the given mesh representation (that is, doesnot form any adjacent mesh elements). Specifically, as an example, ifthe object surface is an open surface (such as that represented by theone of the first 3D crown model 1002 and the second 3D crown model1004), its naked edges may be found at a boundary of the associatedgiven mesh representation.

Thus, the processor 850 may be configured to identify labial naked edges1512 on the labial surface 1502, and lingual naked edges 1514 on thelingual surface 1504. Further, according to some non-limitingembodiments of the present technology, the processor 850 may beconfigured to project the labial naked edges 1512 onto the linguolabialplane 1410, thereby generating a labial edge curve 1602. By the sametoken, the processor 850 may be configured to project the lingual nakededges 1514 onto the linguolabial plane 1410, thereby generating alingual edge curve 1604.

In some non-limiting embodiments of the present technology, theprocessor 850 may further be configured to smooth each one of the labialedge curve 1602 and the lingual edge curve 1604. To that end, theprocessor 850 may be configured to execute one or more smoothingalgorithms, which may include, without being limited to: a kernelsmoothing algorithm (such as an exponential kernel algorithm, forexample), a polynomial smoothing algorithm, a Bezier smoothingalgorithm, and the like.

Finally, according to some non-limiting embodiments of the presenttechnology, using one of the curve fitting techniques describedhereinabove with reference to FIG. 12 in respect of the first averageintersection curve 1210, and based on the labial edge curve 1602 and thelingual edge curve 1604, the processor 850 may be configured to generatethe linguolabial edge curve 1606.

Further, the processor 850 may be configured to determine a linguolabialedge point 1608 on the linguolabial edge curve 1606 for orienting thesecond guide axis 1302 thereto, thereby determining the tooth axis 42.

In some non-limiting embodiments of the present technology, theprocessor 850 may be configured to determine the linguolabial edge point1608 as a maximum point of the linguolabial edge curve 1606 along the Zaxis within the second coordinate system 1107. Accordingly, in thosenon-limiting embodiments of the present technology, which are directedto determining a tooth axis for the given one of the lower teeth 17based on a respective 3D crown model, a respective linguolabial edgepoint may be determined, by the processor 850, as a minimum point of anassociated linguolabial edge curve along the Z axis within theassociated coordinate system.

Finally, according to certain non-limiting embodiments of the presenttechnology, having determined the linguolabial edge point 1608, theprocessor 850 may be configured to modulate a current position of thesecond guide axis 1302 to extend it through the linguolabial edge point1608, thereby determining the tooth axis 42. For example, the processor850 may be configured to rotate the second guide axis 1302 around the Zaxis of the second coordinate system 1107 until it matches thelinguolabial edge point 1608.

Thus, it can be said that the processor 850 may be configured todetermine the tooth axis 42 of the tooth 16 c, based on the second 3Dcrown model 1004 of the crown portion 26, as a line having beengenerated based on the second intersection curve 1312 and extendingthrough the second separation point 1304 and the linguolabial edge point1608.

Determining CR Point

As previously noted, according to the non-limiting embodiments of thepresent technology, the processor 850 may further be configured todetermine the CR point 40 for the tooth 16 c on the tooth axis 42associated therewith. This section equally applies to both Scenario 1and Scenario 2.

In some non-limiting embodiments of the present technology, theprocessor 850 may be configured to determine the CR point 40 on thetooth axis 42 based on dimension data of the tooth 16 c, such as that ofthe crown portion 26 and the root portion 28.

In this regard, the processor 850 may be configured to determine a crownportion height of the crown portion 26 based on one of the first 3Dcrown model 1002 and the second 3D crown model 1004. As previouslymentioned, each of the first 3D crown model 1002 and the second 3D crownmodel 1004 may be represented by a respective plurality of meshelements, where a given mesh element is typically characterized by anumber of vertices and a number of edges. Thus, in some non-limitingembodiments of the present technology, in order to determine the crownportion height, the processor 850 may be configured to project eachvertex of a respective plurality of mesh elements associated with one ofthe first 3D crown model 1002 and the second 3D crown model 1004 ontothe tooth axis 42. Further, the processor 850 may be configured todetermine the crown portion height of the crown portion 26 as adifference in distance between a maximum point and a minimum point (mostdistant ones from each other of the so projected vertices along thetooth axis 42) of a respective one of the first 3D crown model 1002 andthe second 3D crown model 1004 along the tooth axis 42 within arespective one of the coordinate system 1105 and the second coordinatesystem 1107.

In other non-limiting embodiments of the present technology, theprocessor 850 may be configured to determine the crown portion height byconstructing a so-called bounding box around one of the first 3D crownmodel 1002 and the second 3D crown model 1004.

In the context of the present specification, the term “bounding box” isbroadly referred to as a three-dimensional box (or a parallelepiped) ofa smallest possible measure (such as an area or a volume thereof)allowing for entirely enclosing a given point set (such as vertices of arespective plurality of mesh elements associated with one of the first3D crown model 1002 and the second 3D crown model 1004).

With reference to FIG. 17, there is depicted a perspective view of thefirst 3D crown model 1002 enclosed in a bounding box 1702 constructed bythe processor 850 for determining a crown portion height 1704 of thecrown portion 26, in accordance with certain non-limiting embodiments ofthe present technology.

As it can be appreciated from FIG. 17, the crown portion height 1704 maybe determined, by the processor 850 within the coordinate system 1105,as a perpendicular distance between an upper surface 1706 and a lowersurface 1708 of the bounding box 1702. The processor 850 may also beconfigured to determine, within the second coordinate system 1107, amaximum point 1710 and a minimum point 1712 of the first 3D crown model1002 along the tooth axis 42 as respective intersection points betweenthe upper surface 1706 and the lower surface 1708 and the tooth axis 42.

In some non-limiting embodiments of the present technology, theprocessor 850 may be further configured to modulate the crown portionheight 1704 by increasing or decreasing it by a predetermined distance,such 1 mm, for example.

Further, to determine a root portion height of the root portion 28,according to some non-limiting embodiments of the present technology,the processor 850 may be configured to have access to tooth referencedata indicative of approximate tooth heights (or otherwise tooth lengthsaveraged over a certain sample of subjects) of respective ones of theupper teeth 16 and the lower teeth 17. In these embodiments, thereference tooth data may be stored, for example, in the solid-statedrive 860.

TABLE 1 Tooth Reference Data Maxillary Mandibular Total Crown Root TotalCrown Root tooth portion portion tooth portion portion height heightheight height height height Tooth (mL_(t) ± (mL_(c) ± (mL_(r) ± (mL_(t)± (mL_(c) ± (mL_(t) ± number ΔL_(t)), mm ΔL_(c)), mm ΔL_(r)), mmΔL_(t)), mm ΔL_(c)), mm ΔL_(t)), mm 1 22.2 ± 1.9 9.2 ± 1.5 13.0 ± 1.720.3 ± 1.8 7.5 ± 1.3 12.8 ± 1.6 2 21.5 ± 1.8 8.6 ± 1.2 12.9 ± 1.6 21.8 ±1.9 8.2 ± 1.1 13.7 ± 1.6 3 25.6 ± 2.7 9.7 ± 1.4 15.9 ± 2.4 25.1 ± 2.89.8 ± 1.4 15.3 ± 2.1 4 20.7 ± 2.0 7.1 ± 1.0 13.6 ± 1.8 21.5 ± 1.8 7.8 ±1.1 13.7 ± 1.7 5 20.8 ± 2.0 6.7 ± 0.9 14.4 ± 1.9 21.9 ± 1.9 6.7 ± 1.115.2 ± 1.8 6 19.5 ± 1.8 6.2 ± 0.6 13.3 ± 1.7 20.2 ± 1.7 5.8 ± 0.9 14.5 ±1.7 7 19.6 ± 1.9 6.6 ± 0.8 13.0 ± 1.8 20.2 ± 1.7 6.1 ± 0.9 14.1 ± 1.7 818.4 ± 2.0 6.2 ± 0.9 12.2 ± 2.0 18.9 ± 1.9 6.1 ± 0.9 12.8 ± 1.9

Referring to Table 1, there is provided tooth reference data for atleast some of the upper teeth 16 (maxillary) and the lower teeth 17(mandibular) including data of approximate total tooth heights and thatof respective crown portion heights and respective root portion heights.Thus, for example, assuming that the tooth 16 c is a maxillary tooth 3,according to Table 1, and it has been determined that the crown portionheight of the crown portion 26 (such as the crown portion height 1704)is 9.5 mm, the processor 850 may be configured to determine a rootportion height of the root portion 28 to be 15.9±2.4 mm. Further, theprocessor 850 may be configured to determine an absolute root deltavalue of the so determined root portion height of the maxillary tooth 3.For example, according to Table 1, given that the crown portion height1704 of the maxillary tooth 3 is 0.2 mm lower than a mean crown portionheight value mL³ _(c) which is 9.7 mm, the processor 850 may beconfigured to determine a relative crown portion height delta accordingto the following equation:

$\begin{matrix}{{\delta_{c}^{3} = {\frac{\Delta\; L_{c}^{3}}{\Delta\;{Lc}} = {\frac{0.2\mspace{14mu}{mm}}{1.4\mspace{14mu}{mm}} \approx {{0.1}43}}}},} & (2)\end{matrix}$

-   -   where ΔL³ _(c) is an absolute crown portion height delta of the        crown portion height 1704 of the maxillary tooth 3; and    -   ΔL_(c) is an average absolute crown portion height delta for the        maxillary tooth 3.

Further, the processor 850 may be configured to determine the absoluteroot height portion delta for the maxillary tooth 3 according to thefollowing equation:ΔL _(r) ³=δ_(c) ³ ·ΔL _(r)=0.143·2.4 mm≈0.3 mm,  (3)

-   -   where ΔL_(r) is an average absolute root portion height delta        for the maxillary tooth 3.

Thus, the processor 850 may be configured to determine the root portionheight of the root portion 28 in accordance with the following equation:L ³ _(r) =mL ³ _(r) −ΔL ³ _(r)=15.9 mm−0.3 mm=15.6 mm,  (4)

-   -   where mL³ _(r) is a mean root portion height of the maxillary        tooth 3, according to Table 1.

Finally, using the so determined root portion height of the root portion28, the processor 850 may be configured to determine the CR point 40associated with the tooth 16 c on the tooth axis 42.

With reference to FIG. 18, there is depicted a cross-sectionalmesiodistal view of the first 3D crown model 1002 produced, for example,by the first mesiodistal plane 1110, for determining the CR point 40 onthe tooth axis 42 of the tooth 16 c based on a root portion height 1804of the root portion 28, in accordance with certain non-limitingembodiments of the present technology.

In some non-limiting embodiments of the present technology, theprocessor 850 may be configured to render a schematic rootrepresentation 1802 of the root portion 28 based at least on the toothaxis 42, the crown portion height 1704, and the root portion height1804.

Further, according to some non-limiting embodiments of the presenttechnology, based on the root portion height 1804, the processor 850 maybe configured to determine a CR distance 1806, at which the processor850 may further determine the CR point 40 along the tooth axis 42 fromthe first 3D crown model 1002 representative of the crown portion 26.

In some non-limiting embodiments of the present technology, theprocessor 850 may be configured to determine the CR distance 1806according to the following equation:D _(CR) =k·L _(r),  (5)

where D_(CR) is the CR distance 1806;

-   -   k is a proportional coefficient; and    -   L_(r) is the root portion height 1804.

In specific non-limiting embodiments of the present technology, theproportional coefficient k may be 0.5; however, in other non-limitingembodiments of the present technology, other values of the proportionalcoefficient k, such as 0.3 or 0.4, may also be used. Thus, for example,given that the tooth 16 c is the maxillary tooth 3, the CR distance 1806may be determined as 0.5.15.6 mm=8.3 mm.

In some non-limiting embodiments of the present technology, theprocessor 850 may be configured to determine the CR point 40 associatedwith the tooth 16 c, on the tooth axis 42, as a point located thereon atthe CR distance 1806 from the maximum point 1710. Accordingly, in theembodiments of the present technology implemented in respect of therespective one of the lower teeth 17, the processor 850 may beconfigured to determine a respective CR point on the associated toothaxis to be located at a so determined respective CR distance from acorresponding minimum point of the respective 3D crown model.

Thus, having determined a respective CR point for each of the upperteeth 16, the processor 850 may be configured to cause display (forexample, in the screen 722) of each of 3D crown models associated withrespective crown portions of the upper teeth 16 along with so determinedtooth axes and the CR points so determined thereon.

FIG. 19 depicts a plurality of the 3D crown models respectivelycorresponding to the upper teeth 16 and associated with so determinedtooth axes and CR points thereon. Thus, in some non-limiting embodimentsof the present technology, the processor 850 may be configured to usethe tooth axis 42 and the CR point 40 determined thereon for modellingat least some of the tooth movements described above with reference toFIGS. 3 to 6 for planning and/or determining the orthodontic treatmentfor the subject aimed to cause the tooth 16 c to move towards thealigned position.

Given the architecture and the examples provided hereinabove, it ispossible to execute a method for determining CR point for a given tooth(such as the tooth 16 c) for planning an orthodontic treatment for thesubject. With reference to FIG. 20, there is depicted a flowchart of amethod 2000, according to the non-limiting embodiments of the presenttechnology. The method 2000 can be executed by a processor of acomputing environment, such as the processor 850 of the computingenvironment 840.

Step 2002: Receiving Image Data Associated with a Tooth Crown of aPatient

The method 2000 commences at step 2002 where the processor 850 can beconfigured to receive the image data associated with the subject's teeth(for example, the upper teeth 16 or the lower teeth 17). To that end, insome non-limiting embodiments of the present technology, the processor850 may be configured to receive a 3D model representing currentconfiguration of subject's arch forms, such as the 3D model 900 depictedin FIG. 9.

Further, as noted hereinabove, the processor 850 may be configured toapply one or more automatic tooth segmentation algorithms to segment the3D model 900 into a plurality of 3D crown models respectively associatedwith each of the upper teeth 16 and the lower teeth 17, such as one ofthe first 3D crown model 1002 and the second 3D crown model 1004 of thecrown portion 26 associated with the tooth 16 c.

Step 2004: Determining a Tooth Mesh from the Image Data, the Tooth MeshRepresentative of a Surface of the Tooth Crown

At step 2004, according to certain embodiments of the presenttechnology, the processor 850 may be configured to render one of thefirst 3D crown model 1002 and the second 3D crown model 1004 as arespective plurality of mesh elements (such as polygonal meshes)formatted in one of image file formats (such as STL, OBJ, PLY, and thelike).

Step 2006: Identifying an Internal Reference Point in the Image Data,the Internal Reference Point being Based on a Predetermined InternalReference Point Instruction for Locating the Internal Reference Point ina Given Tooth Crown

At step 2006, the method 2000 is directed to starting to analyzecurvature of the crown portion 26 by determining a respectiveintersection curve of one of the first 3D crown model 1002 and thesecond 3D crown model 1004 with a respective mesiodistal plane. To thatend, according to some non-limiting embodiments, the processor 850 maybe configured to determine an origin for constructing the respectivemesiodistal plane as a reference point determined for each of the first3D crown model 1002 and the second 3D crown model 1004 (such as thereference point 1108 associated with the first 3D crown model 1002).

Thus, for determining the reference point 1108, first, the processor 850can be configured to identify a mesial point and a distal point on themesial surface and the distal surface of the first 3D crown portion1002, respectively—such as the distal point 1102 and the mesial point1104 as described above with reference to FIG. 11.

Further, the processor 850 may be configured to join the distal point1102 and the mesial point 1104, thereby generating the mesiodistal line1106 extending through the first 3D crown model 1002. Finally, applyinga predetermined rule, the processor 850 may be configured to determinethe reference point 1108. In some non-limiting embodiments of thepresent technology, the processor 850 may be configured to determine thereference point 1108 as a midpoint of the mesiodistal line 1106.

Further, according to some non-limiting embodiments of the presenttechnology, using so determined the mesiodistal line 1106 and thereference point 1108 thereon, the processor 850 may further beconfigured to define a coordinate system (such as the coordinate system1105) for the first 3D crown model 1102.

By the same token, as described above with reference to FIGS. 13 and 14,for the second 3D crown model 1004, the processor 850 may be configuredto (1) identify the second distal point 1402 and the second mesial point1404; (2) join the second distal point 1402 and the second mesial point1404, thereby generating the second mesiodistal line 1406; and (3)determine, on the second mesiodistal line 1406, the second referencepoint 1308. Further, the processor 850 may be configured to define,based on the second reference point 1308, the second coordinate system1107 for the second 3D crown model 1004.

Step 2008: Determining a Reference Plane in the Image Data, theReference Plane Crossing the Internal Reference Point and the Tooth Meshand being Based on a Predetermined Reference Plane Instruction forLocating the Reference Plane Relative to the Internal Reference Pointfor a Given Tooth

At step 2008, the method 2000 is directed to determining respectivemesiodistal planes, such as the first mesiodistal plane 1110 for thefirst 3D crown model 1002 and the second mesiodistal plane 1320 for thesecond 3D crown model 1004.

To that end, according to certain non-limiting embodiments of thepresent technology, the processor 850 may be configured to determineeach of the first mesiodistal plane 1110 and the second mesiodistalplane 1320 to originate in a respective one of the reference point 1108and the second reference point 1308 and to be perpendicular to arespective one of the mesiodistal line 1106 and the second mesiodistalline 1406.

Step 2010: Determining an Intersection Curve Based on an Intersection ofthe Reference Plane and the Tooth Mesh, the Intersection Curve Followinga Shape of the Surface of the Crown at the Reference Plane

According to certain non-limiting embodiments of the present technology,having determined each of the first mesiodistal plane 1110 and thesecond mesiodistal plane 1320, at step 2010, the processor 850 mayfurther be configured to determine intersection thereof with arespective one of the first 3D crown model 1002 and the second 3D crownmodel 1004, thereby generating the first intersection curve 1112 and thesecond intersection curve 1312, respectively, as described above withreference to FIGS. 11 and 13.

Step 2012: Determining a Tooth Axis of the Tooth Crown Based on theIntersection Curve

At step 2012, the processor 850 is configured to determine the toothaxis 42 for the crown portion 26, based on one of the first intersectioncurve 1112 and the second intersection curve 1312, for furtherdetermining thereon the CR point 40. To that end, according to somenon-limiting embodiments of the present technology, first, the processor850 may be configured to generate a respective guide axis associatedwith each of the first 3D crown model 1002 and the second 3D crown model1004.

In this regard, first, the processor 850 may be configured to segmenteach of the first intersection curve 1112 and the second intersectioncurve 1312, into at least two subcurves (such as the first subcurve 1206and the second subcurve 1208 of the first intersection curve 1112), by arespective separation point, such as the first separation point 1204 andthe second separation point 1304.

According to some non-limiting embodiments of the present technology,the processor 850 may be configured to determine the first separationpoint 1204 as a point on the first intersection curve 1112 closest,within the coordinate system 1105, to the reference point 1108. Further,in other non-limiting embodiments of the present technology, theprocessor 850 may be configured to determine the second separation point1304 as a minimum point of the second intersection curve 1312 within thesecond coordinate system 1107. In these embodiments, a separation pointassociated with a 3D crown model (not separately depicted) of therespective one of the lower teeth 17 may be identified, by the processor850, as a maximum point of an associated intersection curve along a Zaxis within an associated coordinate system.

Further, based on one of the first separation point 1204 and the secondseparation point 1304, the processor 850 may be configured to generatethe first average intersection curve 1210 and the second averageintersection curve 1310, respectively, using one or more curve fittingtechniques, as described above with reference to FIGS. 12 and 13.

Finally, according to some non-limiting embodiments of the presenttechnology, applying the linear regression algorithm to each of thefirst average intersection curve 1210 and the second averageintersection curve 1310, the processor may hence be configured togenerate the first guide axis 1202 and the second guide axis 1302,respectively.

According to some non-limiting embodiments of the present technology,the first guide axis 1202, extending through the first separation point1204, may comprise the tooth axis 42 for the crown portion 26.

According to other non-limiting embodiments of the present technology,the tooth axis 42 may be determined based on the second guide axis 1302by angular modulation thereof in a linguolabial plane (such as thelinguolabial plane 1410) associated with the second 3D crown model 1004.

To that end, according to certain non-limiting embodiments of thepresent technology, the processor 850 may be configured to determine thelinguolabial plane 1410 as a plane parallel to the second mesiodistalline 1406. In alternative non-limiting embodiments of the presenttechnology, the processor 850 may be configured to determine thelinguolabial plane 1410 as a plane parallel to the second mesiodistalline 1406 and perpendicular to the to the second mesiodistal plane 1320as described with reference to FIG. 14.

Further, upon determination of the linguolabial plane 1410, theprocessor 850 may be configured to construct therein a linguolabial edgecurve (such as the linguolabial edge curve 1606). According to certainnon-limiting embodiments of the present technology, the processor 850may be configured to construct the linguolabial edge curve 1606 based onprojecting the labial naked edges 1512 and lingual naked edges 1514 ontothe linguolabial plane 1410 as described above with reference to FIGS.15 and 16.

Finally, by identifying a maximum point (or a minimum point for a givenone of the lower teeth 17) on the linguolabial edge curve 1606 withinthe second coordinate system 1107, the processor 850 may be configuredto determine the linguolabial edge point 1608 and further configured tomodulate a current position of the second guide axis 1302 to extend itthrough the linguolabial edge point 1608, thereby determining the toothaxis 42. For example, the processor 850 may be configured to rotate thesecond guide axis 1302 around the Z axis of the second coordinate system1107 until it matches the linguolabial edge point 1608.

Step 2014: Determining a Crown Height of the Tooth Crown Based on theTooth Axis

According to certain non-limiting embodiments of the present technology,the processor 850 can be configured to determine the CR point 40 on theso determined tooth axis 42 based on the dimension data associated withthe tooth 16 c.

Thus, at step 2014, the processor 850 may be configured to determine thecrown portion height of the crown portion 26 based on one of the first3D crown model 1002 and the second 3D crown model 1004.

In some non-limiting embodiments of the present technology, theprocessor 850 may be configured to determine the crown height portionbased on projecting each vertex of a respective plurality of meshelements associated with one of the first 3D crown model 1002 and thesecond 3D crown model 1004 onto the tooth axis 42. Further, theprocessor 850 may be configured to determine the crown portion height ofthe crown portion 26 as a difference in distance between a maximum pointand a minimum point (most distant ones from each other of the soprojected vertices along the tooth axis 42) of a respective one of thefirst 3D crown model 1002 and the second 3D crown model 1004 along thetooth axis 42 within a respective one of the coordinate system 1105 andthe second coordinate system 1107.

In other non-limiting embodiments of the present technology, theprocessor 850 may be configured to determine the crown height portion ofthe crown portion 26 by constructing therearound a bounding box, such asthe bounding box 1702, as described above with reference to FIG. 17.

In some non-limiting embodiments of the present technology, theprocessor 850 may further be configured to modulate the so determinedcrown portion height by increasing or decreasing it by a predetermineddistance, such 1 mm, for example.

Step 2016: Determining the Center of Resistance of the Tooth Based onthe Determined Crown Height and the Determined Tooth Axis

According to some non-limiting embodiments of the present technology, atstep 2016, first, the processor 850 may be configured to determine theroot portion height of the root portion 28 of the tooth 16 c. To thatend, the processor 850 may have access to tooth reference data, such asthat provided in Table 1. Further, the processor 850 may be configuredto determine the root portion height corresponding to a givenconfiguration of the tooth 16 c and based on the determined crownportion height, using Equations (2) to (4).

Further, based on the so determined root portion height, the processor850 may be configured to determine a distance at which the CR point 40is to be located on the tooth axis 42 from the crown portion 26—such asthe CR distance 1806. The processor 850 may be configured to determinethe CR distance 1806 in accordance with Equation (5).

In specific non-limiting embodiments of the present technology, theprocessor 850 may be configured to determine the CR distance 1806 as ahalf of the root portion height of the root portion 28.

Finally, the processor 850 may be configured to determine the CR point40 associated with the tooth 16 c, on the tooth axis 42, as a pointlocated thereon at the CR distance 1806 from the maximum point (or aminimum point for the given one of the lower teeth 17) associated with arespective one of the first 3D crown model 1002 and the second 3D crownmodel 1004 (such as the maximum point 1710 associated with the first 3Dcrown model 1002).

According to certain non-limiting embodiments of the present technology,applying the method 2000 to crown portions of each of the upper teeth16, the processor 850 may be configured to determine the respective CRpoints associated therewith. Further, as described with reference toFIG. 19, the processor 850 may be configured to cause display (forexample, in the screen 722) of each of 3D crown models associated withrespective crown portions of the upper teeth 16 along with so determinedtooth axes and the CR points so determined thereon. The so depicted 3Dcrown models may further be used for developing the orthodontictreatment for the subject, for example, by modelling, for the tooth 16c, at least some of the tooth movements described above with referenceto FIGS. 3 to 6.

Thus, certain embodiments of the method 2000 allow for a more subject-and tooth-specific determination of a respective tooth axis for each ofthe upper teeth 16 and lower teeth 17, such as the tooth axis 42 for thetooth 16 c, and further determining thereon a respective CR point (suchas the CR point 40) using image data representative only of respectivecrown portions thereof (such as one of the first 3D crown model 1002 andthe second 3D crown model 1004) captured, for example, by a conventionalintraoral scanner. Such an approach may allow for a more accuratemodelling of one of the tooth movements described above with referenceto FIGS. 3 to 6 with a more efficient use of computational resources(that is, without a need for considering additional image data, suchCT/magnetic resonance scans or panoramic radiograph), which mayeventually enable to plan orthodontic treatments more effectively andefficiently at an expected level of accuracy thereof.

The method 2000 hence terminates.

It should be expressly understood that not all technical effectsmentioned herein need to be enjoyed in each and every embodiment of thepresent technology.

Modifications and improvements to the above-described implementations ofthe present technology may become apparent to those skilled in the art.The foregoing description is intended to be exemplary rather thanlimiting. The scope of the present technology is therefore intended tobe limited solely by the scope of the appended claims.

The invention claimed is:
 1. A method for determining a center ofresistance point of a tooth for orthodontic treatment planning, themethod being executable by a processor, the method comprising: obtainingimage data associated with a tooth crown of a patient, the image dataincluding a tooth mesh representative of a surface of the tooth crown;identifying a mesiodistal center of the tooth crown from the image data;determining a reference plane in the image data, the reference planebeing at a predetermined relationship to a mesiodistal line and amesiodistal center, the mesiodistal line comprising a line extendingbetween a mesial side of the tooth crown and a distal side of the toothcrown; determining an intersection curve based on an intersection of thereference plane and the tooth mesh, the intersection curve following ashape of the surface of the crown at the reference plane; determining atooth axis of the tooth crown based on the intersection curve by:bisecting the intersection curve into two intersection curve parts basedon a separation point; generating an average intersection curve usingthe two intersection curve parts; generating, based on the averageintersection curve, a guide axis using a linear regression algorithm;and determining the tooth axis based on the guide axis; determining acrown height of the tooth crown based on the tooth axis; and determiningthe center of resistance of the tooth based on the determined crownheight and the determined tooth axis.
 2. The method of claim 1, whereinthe predetermined relationship of the reference plane to the mesiodistalline comprises the reference plane being perpendicular to themesiodistal line and extending through the mesiodistal center.
 3. Themethod of claim 1, wherein the identifying the internal reference pointcomprises: obtaining a mesial point on the mesial side of the toothcrown, and a distal point on the distal side of the tooth crown;generating the mesiodistal line joining the mesial point and the distalpoint; identifying the mesiodistal center as a midpoint on themesiodistal line.
 4. The method of claim 1, wherein if the tooth is apremolar tooth or a molar tooth, the separation point comprises: a pointon the intersection curve which is closest to the internal referencepoint, and the tooth axis is determined as the guide axis.
 5. The methodof claim 1, wherein if the tooth is an incisor tooth or a canine tooth,the separation point comprises: for maxillary teeth, a minimum point ofthe intersection curve along a Z axis direction for maxillary teeth; andfor mandibular teeth, a maximum point of the intersection curve in a Zaxis direction for mandibular teeth.
 6. The method of claim 5, whereinthe determining the tooth axis comprises: determining a linguolabialreference plane which is parallel to the mesiodistal line; dissectingthe surface of the tooth crown, by the linguolabial reference plane,into a lingual surface and a labial surface; identifying lingual nakededges on the lingual surface of the surface of the tooth crown;identifying labial naked edges on the labial surface of the surface ofthe tooth crown; generating a lingual edge curve based on projecting thelingual naked edges onto the linguolabial reference plane; generating alabial edge curve based on projecting the labial naked edges onto thelinguolabial reference plane; generating, based on the lingual edgecurve and the labial edge curve, an average linguolabial edge curve;determining a linguolabial edge point, the determining comprises: formaxillary teeth, identifying a maximum point of the linguolabial edgecurve along a Z axis associated with the linguolabial reference plane;and for mandibular teeth, identifying a minimum point of thelinguolabial edge curve along the Z axis associated with thelinguolabial reference plane; and determining the tooth axis by rotatingthe guide axis around the Z axis associated with the linguolabialreference plane until it matches the linguolabial edge point on thelinguolabial plane.
 7. The method of claim 4, wherein the determiningthe crown height comprises generating a bounding box around the toothmesh and along the determined tooth axis, and determining the crownheight as a height of the tooth mesh along the tooth axis.
 8. The methodof claim 4, wherein the determining the crown height comprisesprojecting tooth mesh vertices of the tooth mesh onto the tooth axis,and determining a distance difference between a minimum point andmaximum point along the tooth axis.
 9. The method of claim 1, furthercomprising modulating the determined crown height by a predetermineddistance.
 10. The method of claim 1, wherein the determining the centerof resistance of the tooth based on the determined crown height and thedetermined tooth axis comprises: retrieving, from a memory, anapproximate root length based on the determined crown height; dividingthe approximate root length by two to define a center of resistancedistance; determining the center of resistance of the tooth as a pointalong the tooth axis at a distance relating to the center of resistancedistance from a crown start point.
 11. The method of claim 1, whereinthe image data is associated with a plurality of teeth of the patient,and the method further comprises segmenting the image data to obtain aseparate tooth mesh for each one of the plurality of teeth.
 12. Themethod of claim 1, further comprising displaying the image data and oneor both of the determined tooth axis and the determined center ofresistance.
 13. The method of claim 1, further comprising determining anorthodontic treatment using the determined center of resistance.
 14. Amethod for determining a center of resistance point of a tooth fororthodontic treatment planning, the method being executable by aprocessor, the method comprising: obtaining image data associated with atooth crown of a patient, the image data including a tooth meshrepresentative of a surface of the tooth crown; identifying an internalreference point in the image data, the internal reference point beingbased on a predetermined internal reference point instruction forlocating the internal reference point in a given tooth crown;determining a reference plane in the image data, the reference planecrossing the internal reference point and the tooth mesh and being basedon a predetermined reference plane instruction for locating thereference plane relative to the internal reference point for a giventooth; determining an intersection curve based on an intersection of thereference plane and the tooth mesh, the intersection curve following ashape of the surface of the crown at the reference plane; determining atooth axis of the tooth crown based on the intersection curve by:bisecting the intersection curve into two intersection curve parts basedon a separation point; generating an average intersection curve usingthe two intersection curve parts; generating, based on the averageintersection curve, a guide axis using a linear regression algorithm;and determining the tooth axis based on the guide axis; determining acrown height of the tooth crown based on the tooth axis; and determiningthe center of resistance of the tooth based on the determined crownheight and the determined tooth axis.
 15. The method of claim 14,wherein the internal reference point comprises a mesiodistal center ofthe tooth crown, the identifying the internal reference pointcomprising: obtaining a mesial point on a mesial side of the toothcrown, and a distal point on a distal side of the tooth crown,generating a mesiodistal line joining the mesial point and the distalpoint; and identifying the mesiodistal center as a midpoint on themesiodistal line.
 16. The method of claim 15, wherein the referenceplane is perpendicular to the mesiodistal line and extends through themesiodistal center.
 17. The method of claim 14, wherein if the tooth isa premolar tooth or a molar tooth, the separation point comprises: apoint on the intersection curve which is closest to the internalreference point, and the tooth axis is determined as the guide axis; andif the tooth is an incisor tooth or a canine tooth, the separation pointcomprises: for maxillary teeth, a minimum point of the intersectioncurve along a Z axis direction for maxillary teeth; and for mandibularteeth, a maximum point of the intersection curve in a Z axis directionfor mandibular teeth.
 18. The method of claim 17, wherein thedetermining the tooth axis comprises: determining a linguolabialreference plane which is parallel to the mesiodistal line; dissectingthe surface of the tooth crown, by the linguolabial reference plane,into a lingual surface and a labial surface; identifying lingual nakededges on the lingual surface of the surface of the tooth crown;identifying labial naked edges on the labial surface of the surface ofthe tooth crown; generating a lingual edge curve based on projecting thelingual naked edges onto the linguolabial reference plane; generating alabial edge curve based on projecting the labial naked edges onto thelinguolabial reference plane; generating, based on the lingual edgecurve and the labial edge curve, an average linguolabial edge curve;determining a linguolabial edge point, the determining comprises: formaxillary teeth, identifying a maximum point of the linguolabial edgecurve along a Z axis associated with the linguolabial reference plane;and for mandibular teeth, identifying a minimum point of thelinguolabial edge curve along the Z axis associated with thelinguolabial reference plane; determining the tooth axis by rotating theguide axis around the Z axis associated with the linguolabial referenceplane until it matches the linguolabial edge point on the linguolabialplane.
 19. A system for determining a center of resistance point of atooth for orthodontic treatment planning, the system comprising aprocessor arranged to execute a method, the method comprising: obtainingimage data associated with a tooth crown of a patient, the image dataincluding a tooth mesh representative of a surface of the tooth crown;identifying an internal reference point in the image data, the internalreference point being based on a predetermined internal reference pointinstruction for locating the internal reference point in a given toothcrown; determining a reference plane in the image data, the referenceplane crossing the internal reference point and the tooth mesh and beingbased on a predetermined reference plane instruction for locating thereference plane relative to the internal reference point for a giventooth; determining an intersection curve based on an intersection of thereference plane and the tooth mesh, the intersection curve following ashape of the surface of the crown at the reference plane; determining atooth axis of the tooth crown based on the intersection curve by:bisecting the intersection curve into two intersection curve parts basedon a separation point; generating an average intersection curve usingthe two intersection curve parts; generating, based on the averageintersection curve, a guide axis using a linear regression algorithm;and determining the tooth axis based on the guide axis; determining acrown height of the tooth crown based on the tooth axis; and determiningthe center of resistance of the tooth based on the determined crownheight and the determined tooth axis.